# “Dockside Math”, A2+B2=C2

Tying up the boat using “Dockside Math”, A2+B2=C2

When tying up along side a dock, you will more than likely hang a fender over the side at amidships up against a dock post. You will want to keep the boat in place on the dock post, yet allow for the tidal drop. If you try to do this with bow and stern lines, and add enough slack for tidal swings, the fender won’t stay in place on the dock post. It will move one way or the other resulting in scratched up topsides.

The solution is spring lines, one going forward, and one going aft. These springs can be made fairly snug if they are long enough, and still allow for a tidal drop. The lines should be fastened to the dock near the ends of the boat, and can be lead back to a cleat, or winch on the other end of the boat. Snug these up against each other. Adjust the bow and stern lines so that the ends of the boat can’t touch the dock. Leave enough slack in these to account for the tidal drop. Consider running the stern line to the side of the stern that is not up against the dock. The rule of thumb is that the longer the lines are, the less slack you’ll need in them.

Do you remember the Pythagorean Theorem from your eight grade math class, A2+b2=c2? I bet you thought you’d never have use for it, and it was a waste of brain space when there were so many other things to learn, like how to shoot toothpicks from a straw, or how to stick a pencil in the ceiling tile, or how to ask a girl out without really asking her out. Well, I finally found a use for it in my line of work, which is sailing. My math teacher, Mr. Humphreys would be so proud of me if he knew.

For those captains out there that want the math, here is a calculation for a 35 foot spring line and a 3 foot tidal drop. Where A is the length of the spring line from the dock cleat to your boat cleat, B is the tidal drop, and the resulting C will be the length the line needs to be to allow enough slack for the tidal drop. A2+b2=c2, 352 x 32 =1234, the square root of 1234 is 35.128 feet. So as you can see, for a three foot drop you’d need only two inches of slack in the spring line. This is probably a lot less slack than you would have thought. Line will stretch too, so you will even have a fudge factor built in. This will keep the boat squarely on her fender.

Using this formula for a three foot tide assumes that your dock lines are fairly horizontal. If your lines are exactly horizontal at mid tide, then the 3 foot drop is really a 1 ½ foot swing in either direction, and therefore, the lines can be even more snug, with only one inch of slack. If you are tying your dock lines up near the top of the dock pilings, which is not entirely best, then this formula will not work for you. You will have to have much more slack in the dock lines.

Now do the math for the stern line, it’s only 10 feet long. 102 x 32 = 109, the square root of 109 is 10.44, or 10 feet, 5 inches. Again, a lot less slack than you might have though. Use this thinking to keep your boat out of your neighbor’s slip too. I’ve seen a lot of boats in their slips with very loose dock lines, particularly those boats with their lines tied high on the pilings.